Unit commitment method considering security region of wind turbine generator with frequency response control

ABSTRACT

The present invention discloses a unit commitment method considering security region of wind turbine generators with frequency response control, and the main steps are: 1) determining security region of wind turbine generators when provides frequency response; 2) based on the security region of the wind turbine generators when provides frequency response, establishing a unit commitment model considering security region of wind turbine generators; and 3) calculating the unit commitment model considering the security region of the wind turbine generators by using mixed-integer linear programming method, and obtaining the operation result of the unit commitment considering the security region of the wind turbine generators with frequency response control. The present invention can be widely used in the setting of frequency response parameters of wind turbine generators dispatched in the prior art and the start-stop and output plans of synchronous generator.

FIELD OF THE INVENTION

The present invention relates to the technical filed of electric powersystem and automation, and specifically is unit commitment methodconsidering security region of wind turbine generators with frequencyresponse control.

BACKGROUND OF THE INVENTION

To achieve low-carbon operation of the power system, renewable energysources such as wind power and photovoltaics have developed rapidly.However, in traditional control modes, renewable energy sources, such aswind power and photovoltaics are all non-synchronous energy sources.High-penetration non-synchronous energy sources bring major challengesto system frequency security. The low inertia power system is easy to beinterfered, which will cause the system frequency drop rapidly after afailure, and seriously threaten the system frequency stability. Toensure the system frequency stability, maintaining a certain amount ofsynchronous generator is necessary. But it will limit the penetrationrate of non-synchronous energy sources, and may lead to the consumptionproblem of renewable energy sources. Therefore, renewable energy sourcesare required to undertake the task of providing frequency response.Among renewable energy sources, wind turbine generator is considered asan ideal frequency response provider due to the rotational kineticenergy stored on the rotors. The frequency response control of windturbine generators can simulate frequency response characteristics ofsynchronous generator, such as inertial response and primary frequencyresponse. When determining the scheme of unit commitment, the frequencyresponses of wind turbine generators are expected to reduce the burdenof synchronous generator to provide frequency response. However, theability of wind turbine generators to provide frequency response isrestricted by its safe operation requirement. In thefrequency-constrained unit commitment model, the safety of wind turbinegenerators is usually ignored, leading to the overestimation of thefrequency response capability of wind turbine generators. Therefore, theunit commitment model considering the safety of wind turbine generatorsneeds further study.

SUMMARY OF THE INVENTION

The purpose of the present invention is to solve the problem in theprior art.

The technical solution adopted to achieve the purpose of the presentinvention is as follows. Unit commitment method considering securityregion of wind turbine generator with frequency response control, mainlycomprises the following steps.

1) Determining the Security Region of the Wind Turbine Generators whenProvides Frequency Response, and the Main Steps are as Follows.

1.1) Establishing an Output Model of Wind Turbine Generators whenProvides Frequency Response, Namely:

$\begin{matrix}{{\Delta P_{w}^{PFR}} = {K_{w}\Delta f{and}}} & (1)\end{matrix}$ $\begin{matrix}{{\Delta P_{w}^{IR}} = {J_{w}{\frac{d\Delta f}{dt}.}}} & (2)\end{matrix}$

In the above formulas, ΔP_(w) ^(PFR) and ΔP_(w) ^(IR) respectivelyrepresent the primary frequency response and virtual inertia responseprovided by the wind turbine generators. Frequency response coefficientK_(w)=1/K_(droop-w). K_(droop-w) is the droop control parameter of thewind turbine generators in primary frequency response control. J_(w) isthe virtual inertia control parameter of the wind turbine generators. Δfis the system frequency deviation, and t refers to time.

1.2) Establishing Constraint Condition of the Rotor Rotational Speedω_(r), Namely:ω_(min)≤ω_(r)≤ω_(max)  (3)

In the above formulas, ω_(min) and ω_(max) respectively are the lowestspeed and highest speed of the rotor rotational speed of the windturbine generators.

1.3) Establishing Constraint Conditions of Wind Power Stability, theMain Steps are as Follows.

1.3.1) Determining the Synchronization Characteristics of the WindTurbine Generators, Namely:

$\begin{matrix}{P_{E} = {{K_{DL}\omega_{r}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}{and}}}} & (4)\end{matrix}$ $\begin{matrix}{P_{E} = {P_{M} = {0.5\rho\pi R^{2}{C_{P}\left( {\beta,\lambda} \right)}{v^{3}.}}}} & (5)\end{matrix}$

In the above formulas, P_(E) is the active output of the wind turbinegenerators. K_(DL) is the de-load factor of the wind turbine generators.When the wind turbine generators are working at maximum power trackingmode, the coefficient K_(DL) is the maximum power tracking coefficient,and K_(DL)ω_(r) ³ is the output of the wind turbine generators whenthere is no virtual inertia response. ρ is the air density. R is thediameter of the rotor of the wind turbine generators. ν is the windspeed. C_(p) is the power coefficient of the wind turbine generators.P_(M) is the mechanical power of the wind turbine generators. β is thepitch angle of the wind turbine generators.

Wherein, the tip speed ratio λ is shown as follows.

$\begin{matrix}{\lambda = \frac{R\omega_{r}}{v}} & (6)\end{matrix}$

1.3.2) Determining the limit operating rotational speed ω_(rc) of thewind turbine generators. The limit operating rotational speed ω_(rc) ofthe wind turbine generators meets the following formula.

$\begin{matrix}{\frac{\partial\left( {{K_{DL}\omega_{r}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \right)}{\partial\omega_{r}} = \frac{\partial\left( {0.5{\rho\pi}R^{2}{C_{p}\left( {\beta,\frac{R\omega_{r}}{v}} \right)}v^{3}} \right)}{\partial\omega_{r}}} & (7)\end{matrix}$

1.3.3) Substituting the limit operating rotational speed ω_(rc) of thewind turbine generators into formula (5), calculating to obtain thelimit operating point of the wind turbine generators

$\left( {\omega_{rc},{0.5{\rho\pi}R^{2}{C_{P}\left( {\beta,\frac{R\omega_{rc}}{v}} \right)}v^{3}}} \right).$

1.3.4) Connecting the extreme operating points at each wind speed toform the stability boundary of the wind turbine generators, andsubstituting formula (6) into formula (7) to calculate the limit tipspeed ratio A. The limit tip speed ratio A meets the following formula.

$\begin{matrix}{{3{K_{DL}\left( \frac{\lambda v}{R} \right)}^{2}} = {{{0.5}\rho\pi R^{2}\frac{\partial\left( {C_{P}\left( {\beta,\lambda} \right)} \right)}{\partial\frac{\lambda v}{R}}v^{3}} = {{0.5}\rho\pi R^{3}\frac{\partial\left( {C_{P}\left( {\beta,\lambda} \right)} \right)}{\partial\lambda}v^{2}}}} & (8)\end{matrix}$

1.3.5) Establishing the expression formula of the relationship betweenwind speed and rotor rotational speed on the stability boundary of thewind turbine generators, namely:

$\begin{matrix}{v = {\frac{R\omega_{r}}{\lambda_{c}}.}} & (9)\end{matrix}$

1.3.6) Substituting formula (9) into formula (5), and calculating toobtain the expression formula of the stability boundary of the windturbine generators, namely:

$\begin{matrix}{{P_{c} = {{\frac{{0.5}\rho\pi R^{5}{C_{P}\left( {\beta,\lambda_{c}} \right)}}{\lambda_{c}^{3}}\omega_{r}^{3}} = {K_{c}\omega_{r}^{3}}}}.} & (10)\end{matrix}$

1.3.7) Based on formula (10), updating the limit operating point of thewind turbine generators to (ω_(rc), K_(c)ω_(r) ³).

1.3.8) Establishing the stability constraints of the wind turbinegenerators when provides frequency response, and it is divided into thefollowing three situations.

I) When the wind turbine generators are operating at the lowest speed,the wind turbine generators do not provide frequency response. Thefrequency response of the wind turbine generators is as follows.

$\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} = {{0\omega_{r0}} < \omega_{\min}}} & (11)\end{matrix}$

In the above formulas, ω_(r0) is the rotor rotational speed in theinitial operating state of the wind turbine generators.

II) When the limit operating rotational speed ω_(rc) is less than thelowest speed ω_(min), the stability constraints of the wind turbinegenerators when provides frequency response are as follows.

$\begin{matrix}{{{K_{DL}\omega_{\min}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{f_{M}\left( \omega_{\min} \right)}\omega_{rc}} < \omega_{\min}} & (12)\end{matrix}$

In the above formulas, f_(M)(ω_(min)) is the mechanical power of thewind turbine generators at the lowest rotational speed comm.

III) When ω_(rc)≥ω_(min), the stability constraints of the wind turbinegenerators when provides frequency response are as follows.

$\begin{matrix}{{{K_{DL}\omega_{rc}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {K_{c}\omega_{rc}^{3}}} & (13)\end{matrix}$

1.4) Establishing the output constraints of the wind turbine generatorswhen provides frequency response, and the main steps are as follows.

1.4.1) Updating the active output P_(E)* of the wind turbine generators,namely:

$\begin{matrix}{P_{E}^{\star} = {{\left( {1 - d_{w}} \right)P_{w}} - {K_{w}\Delta f} - {J_{w}{\frac{d\Delta f}{dt}.}}}} & (14)\end{matrix}$

In the above formulas, P_(w) is the available power of the wind turbinegenerators. d_(w) is the reserve coefficient of the wind turbinegenerators, and (1−d_(w))P_(w), is the actual output of the wind turbinegenerators when does not provide frequency response output.

1.4.2) Establishing the output constraints of the wind turbinegenerators when provides frequency response, namely:

$\begin{matrix}{{{\left( {1 - d_{w}} \right)P_{w}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {P_{w}^{\max}.}} & (15)\end{matrix}$

In the above formulas, P_(w) ^(maxis) the maximum output of wind turbinegenerators.

1.5) Combining formula (10), formula (12), formula (13) and formula(15), the security region of the wind turbine generators meets formula(16) to formula (19), namely:

$\begin{matrix}{{K_{w} = 0};{J_{w} = {{0\omega_{r0}} < \omega_{\min}}};} & (16)\end{matrix}$ $\begin{matrix}{{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}\omega_{rc}}} < \omega_{\min}};} & (17)\end{matrix}$ $\begin{matrix}{{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}\omega_{rc}}} \geq \omega_{\min}};{and}} & (18)\end{matrix}$ $\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {P_{w}^{\max} - {\left( {1 - d_{w}} \right){P_{w}.}}}} & (19)\end{matrix}$

2) Based on the security region of the wind turbine generators whenprovides frequency response, establishing a unit commitment modelconsidering the security region of the wind turbine generators. The mainsteps are as follows.

2.1) With the goal of minimizing the operating cost of the traditionalsynchronous generator, establishing the objective function, namely:

$\begin{matrix}{\min{\sum\limits_{i = 1}^{T}{\sum\limits_{g \in \zeta}{\left\lbrack {{\left( {{c_{g}P_{g,i}} + {c_{g}^{nl}N_{g,i}^{on}}} \right)\Delta t} + {c_{g}^{su}N_{g,i}^{su}}} \right\rbrack.}}}} & (20)\end{matrix}$

In the above formulas, cis a set of traditional synchronous generators.c_(g) is the marginal cost. c_(g) ^(nl) is the no-load cost. c_(g) ^(su)is the start-up cost. P_(g,i) is the active power of the traditionalsynchronous generator. N_(g,i) ^(on) is an online synchronous generator.N_(g,i) ^(su) is the synchronous generator turned on at step i. T is thetotal optimization time scale. Δt is the unit time interval. Variableswith the subscript i represent the variables of the i-th step. Variableswith subscript g represent variables related to traditional synchronousgenerator g. Variables with subscripts g,i represent the relatedvariables of the traditional synchronous generator g at the i-th step.

2) Establishing constraints of traditional unit commitment, whichinclude power flow constraints, synchronous generator constraints,system frequency stability constraints, frequency change rateconstraints, frequency lowest point constraints, and wind turbinegenerators security region constraints.

2.2.1) Power flow constraints are as follows.

$\begin{matrix}{{{\sum\limits_{g \in \zeta}P_{g,i}} + {\sum\limits_{w \in W}{\left( {1 - d_{w,i}} \right)P_{w,i}}}} = {{L_{i}i} \in T}} & (21)\end{matrix}$

In the above formulas, W is a set of wind turbine generators. L_(i) isthe total load of the system. The wind turbine generators parameters areall aggregate parameters. Variables with subscript w represent variablesrelated to wind turbine generators w. Variables with subscripts w,irepresent related variables of wind turbine generators w at step i.

2.2.2) Synchronous generator constraints are shown in formula (22) toformula (28).

$\begin{matrix}{{N_{g,i}^{on}P_{g}^{\min}} \leq P_{g,i} \leq {N_{g,i}^{on}P_{g}^{\max}}} & (22)\end{matrix}$ $\begin{matrix}{N_{g,i}^{on} = {N_{g,{i - 1}}^{on} + N_{g,i}^{su} - N_{g,i}^{sd}}} & (23)\end{matrix}$ $\begin{matrix}{N_{g,i}^{off} = {N_{g,{i - 1}}^{off} + N_{g,i}^{sd} - N_{g,i}^{su}}} & (24)\end{matrix}$ $\begin{matrix}{{P_{g,i} - P_{g,{i - 1}}} \leq {{\Delta P_{g}^{\max}N_{g,{i - 1}}^{on}} + {\Delta{P_{g}^{{su}\max}\left( {N_{g,i}^{on} - N_{g,{i - 1}}^{on}} \right)}}}} & (25)\end{matrix}$ $\begin{matrix}{{P_{g,i} - P_{g,{i - 1}}} \geq {{{- \Delta}P_{g}^{\max}N_{g,i}^{on}} + {\Delta P_{g}^{{sd}\max}\left( {N_{g,{i - 1}}^{on} - N_{g,i}^{on}} \right)}}} & (26)\end{matrix}$ $\begin{matrix}{{\sum\limits_{k = {i + 1 - {\Delta t_{g}^{up}}}}^{i}N_{g,k}^{su}} \leq N_{g,i}^{on}} & (27)\end{matrix}$ $\begin{matrix}{{\sum\limits_{k = {i + 1 - {\Delta t_{g}^{dw}}}}^{i}N_{g,k}^{sd}} \leq N_{g,i}^{off}} & (28)\end{matrix}$

In the above formulas, P_(g) ^(min) and P_(g) ^(max) are the minimumvalue and maximum value of the synchronous generator output,respectively. ΔP_(g) ^(max) is the maximum value of the output change ofthe synchronous generator. ΔP_(g) ^(su max) and ΔP_(g) ^(sd max) are themaximum upward and downward climbing power of the synchronous generator,respectively. N_(g,i) ^(sd) is the number of synchronous generators shutdown in the step i. N_(g,i) ^(off) is the number of synchronousgenerators offline at step i. Δt_(g) ^(up) and Δt_(g) ^(dw) are theminimum start and stop time of the unit. i∈T. g∈ζ

2.2.3) The system frequency stability constraints are as follows.

$\begin{matrix}{{{2H_{i}\frac{d\Delta f}{dt}} + {\left( {{D_{i}L_{i}} + K_{i}} \right)\Delta f}} = {{- \Delta}L_{i}}} & (29)\end{matrix}$

Wherein, D_(i) is the load damping coefficient. H_(i) is the systeminertia time constant. K_(i) is the frequency response coefficient.

Wherein, the system inertia time constant H_(i) is shown as follows.

$\begin{matrix}{H_{i} = {\frac{\sum\limits_{g \in \varsigma}{H_{g}P_{g}^{\max}N_{g,i}^{on}}}{f_{0}} + {\pi{\sum\limits_{w \in W}J_{w,i}}}}} & (30)\end{matrix}$

In the above formulas, H_(g) is the inertia time coefficient ofsynchronous generator. The optimized variables in formula (30) are thevirtual inertia control parameters J_(w,i) of the online synchronousgenerator N_(g,i) ^(on) and the wind turbine generators at i-th step. f₀is the reference frequency of the power system.

Frequency response coefficient K_(i) is shown as follows.

$\begin{matrix}{K_{i} = {\frac{\sum\limits_{g \in \varsigma}{K_{g}P_{g}^{\max}N_{g,i}^{on}}}{f_{0}} + {2\pi{\sum\limits_{w \in W}K_{w,i}}}}} & (31)\end{matrix}$

In the above formulas, K_(g)=1/K_(droop-g). K_(droop-g) is the droopcontrol parameter of the synchronous generator. The optimized variablesin formula (31) are the frequency response parameter K_(w,i) of theonline synchronous generator N_(g,i) ^(on) and the wind turbinegenerators at the i-th step.

System frequency deviation Δf is shown as follows.

$\begin{matrix}{{\Delta{f(t)}} = \frac{\left( {e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t} - 1} \right)\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} & (32)\end{matrix}$

Frequency change rate dΔf/dt is shown as follows.

$\begin{matrix}{\frac{d\Delta{f(t)}}{dt} = {{- \frac{\Delta L_{i}}{2H_{i}}}e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}}} & (33)\end{matrix}$

2.2.4) Frequency change rate constraints are shown as follows.

$\begin{matrix}{{❘\left( \frac{d\Delta{f(t)}}{dt} \right)❘} \leq \frac{\Delta L_{i}}{2H_{i}} \leq \left( \frac{d\Delta f}{dt} \right)_{\max}} & (34)\end{matrix}$

2.2.5) Frequency lowest point constraints are shown as follows.

$\begin{matrix}{{{❘{\Delta{f(t)}}❘} \leq {❘{\Delta f_{{nadir},i}}❘}} = {\frac{\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)} \leq {\Delta f_{\max}}}} & (35)\end{matrix}$

2.2.6) Based on formula (1), formula (2), formula (32) to formula (35),establishing the equation of frequency response provided by the windturbine generators, namely:

$\begin{matrix}{{{{- K_{w,i}}\Delta{f(t)}} - {J_{w,i}\frac{d\Delta{f(t)}}{dt}}} = {{{{- K_{w,i}}\frac{\left( {e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t} - 1} \right)\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} + {J_{w,i}\frac{\Delta L_{i}}{2H_{i}}e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}}} = {{{\left( {{- \frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} + \frac{J_{w,i}\Delta L_{i}}{2H_{i}}} \right)e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}} + \frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} \leq {\max\left\{ {\frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)},\frac{J_{w,i}\Delta L_{i}}{2H_{i}}} \right\}} \leq {\max{\left\{ {{K_{w,i}\Delta f_{\max}},{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max}} \right\}.}}}}} & (36)\end{matrix}$

2.2.7) Substituting formula (36) into formula (17) to formula (19) toestablish the security region constraints of the wind turbinegenerators, which are shown as formula (37) to formula (43)respectively.

$\begin{matrix}{{K_{w} = 0};{J_{w} = {{0\omega_{r0}} < \omega_{\min}}}} & (37)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}\omega_{rc}}} < \omega_{\min}} & (38)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}\omega_{rc}}} < \omega_{\min}} & (39)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}\ \omega_{rc}}} \geq \omega_{\min}} & (40)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}\omega_{rc}}} \geq \omega_{\min}} & (41)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {P_{w}^{\max} - {\left( {1 - d_{w,i}} \right)P_{w,i}}}} & (42)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {P_{w}^{\max} - {\left( {1 - d_{w,i}} \right)P_{w,i}}}} & (43)\end{matrix}$

3) Calculating the unit commitment model considering the security regionof the wind turbine generators by using mixed-integer linear programmingmethod, to obtain the operation result of the unit commitmentconsidering the wind turbine generators security region with frequencyresponse control.

It is worth noting that the present invention considers thesynchronization stability of the wind turbine generators, derives thestability constraints of the wind turbine generators, and provides acalculable quantitative expression. Combining the rotational speedconstraints and output constraints of the wind turbine generators,jointly characterize the security region of the wind turbine generatorswhen provides frequency response. Then, according to the characteristicsof the wind turbine generators when provides frequency response (inertiaresponse and primary frequency response), combined with the systemfrequency constraints, linearize the security region of the wind turbinegenerators when provides frequency response, and introduce thelinearized security region into the unit commitment model consideringfrequency constraints. Thus, it can be ensured that the unit commitmentmodel proposed by the present invention can simultaneously meet thesystem frequency constraints and the security region constraints of thewind turbine generators. The frequency response of the wind turbinegenerators obtained based on the present invention can guide the settingof the frequency response control parameter of the wind turbinegenerators.

The technical effect of the present invention is beyond doubt. Thepresent invention has the following effects.

1) The security region of the wind turbine generators when providesfrequency response proposed by the present invention, can effectivelyguide the setting of the frequency response control parameters of thewind turbine generators, ensure the safe and stable operation of thewind turbine generators when provides frequency response, and take intoaccount the stability of the system frequency and the safety of the windturbine generators.

2) The present invention considers both the system frequency stabilityconstraints and the wind turbine generator's own safety constraints inthe unit commitment model. When performing unit dispatch, based on thesafe and stable operation of the wind turbine generators can be ensured,the wind turbine generators can provide frequency response for thesystem, support system frequency stability, reduce the burden ofsynchronous generator to support frequency stability, and save systemoperating costs.

The present invention can be widely used in the setting of frequencyresponse parameters of wind turbine generators dispatched in the priorart and the start-stop and output plans of synchronous generator.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of the security region of the wind turbinegenerators when provides frequency response.

FIG. 2 is a schematic diagram of wind speed.

FIG. 3 is a schematic diagram of system frequency indicators.

FIG. 4 is a schematic diagram of the influence of the security region ofthe wind turbine generators on the frequency response output of the windturbine generators.

FIG. 5 is a schematic diagram of the influence of the reserve capacityof the wind turbine generators on the frequency response output of thewind turbine generators.

DETAILED DESCRIPTION OF THE INVENTION

The present invention will be further described below in conjunctionwith embodiments, but it should not be understood that the scope of theabove subject matter of the present invention is limited to thefollowing embodiments. Without departing from the above-mentionedtechnical idea of the present invention, various substitutions andchanges based on common technical knowledge and conventional means inthe field shall be included in the protection scope of the presentinvention.

Embodiment 1

Refer to FIG. 1 to FIG. 5 , the unit commitment method consideringsecurity region of wind turbine generators with frequency responsecontrol, mainly comprises the following steps.

1) Determining the security region of the wind turbine generators whenprovides frequency response, and the main steps are as follows.

1.1) Establishing an output model of wind turbine generators whenprovides frequency response, namely:

$\begin{matrix}{{\Delta P_{w}^{PFR}} = {K_{w}\Delta f{and}}} & (1)\end{matrix}$ $\begin{matrix}{{\Delta P_{w}^{IR}} = {J_{w}{\frac{d\Delta f}{dt}.}}} & (2)\end{matrix}$

In the above formulas, ΔP_(w) ^(PFR) and ΔP_(w) ^(IR) respectivelyrepresent the primary frequency response and virtual inertia responseprovided by the wind turbine generators. Frequency response coefficientK_(w)=1/K_(droop-w). K_(droop-w) is the droop control parameter of thewind turbine generators in primary frequency response control. J_(w) isthe virtual inertia control parameter of the wind turbine generators. Δfis the system frequency deviation, and t refers to time.

1.2) Establishing constraint condition of the rotor rotational speedω_(r), namely:ω_(min)≤ω_(r)≤ω_(max)  (3)

In the above formulas, ω_(min) and ω_(max) respectively are the lowestspeed and highest speed of the rotor rotational speed of the windturbine generators.

1.3) Establishing constraint conditions of wind power stability, themain steps are as follows.

1.3.1) Determining the synchronization characteristics of the windturbine generators, namely:

$\begin{matrix}{P_{E} = {{K_{DL}\omega_{r}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}{and}}}} & (4)\end{matrix}$ $\begin{matrix}{P_{E} = {P_{M} = {{0.5}\rho\pi R^{2}{C_{P}\left( {\beta,\lambda} \right)}{v^{3}.}}}} & (5)\end{matrix}$

In the above formulas, P_(E) is the active output of the wind turbinegenerators. K_(DL) is the de-load factor of the wind turbine generators.When the wind turbine generators are working at maximum power trackingmode, the coefficient K_(DL) is the maximum power tracking coefficient,and K_(DL)ω_(r) ³ is the output of the wind turbine generators whenthere is no virtual inertia response. ρ is the air density. R is thediameter of the rotor of the wind turbine generators. ν is the windspeed. C_(p) is the power coefficient of the wind turbine generators.P_(M) is the mechanical power of the wind turbine generators. β is thepitch angle of the wind turbine generators.

Wherein, the tip speed ratio λ is shown as follows.

$\begin{matrix}{\lambda = \frac{R\omega_{r}}{v}} & (6)\end{matrix}$

1.3.2) At a certain wind speed, the stability condition of the windturbine generator is that the curve of formula (4) and the curve offormula (5) have at least one intersection, otherwise the wind turbinegenerators may lose its balance point and cause instability. Therefore,the stability limit of the wind turbine generators is that the curve offormula (4) and the curve of formula (5) have one and only oneintersection point, which is the tangent point of the curve of formula(4) and the curve of formula (5). Therefore, the limit operating speedω_(rc) of the wind turbine generators is calculated by deriving formula(4) and formula (5).

$\begin{matrix}{\frac{\partial\left( {{K_{DL}\omega_{r}^{2}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \right)}{\partial\omega_{r}} = \frac{\partial\left( {0.5{\rho\pi}R^{2}{C_{p}\left( {\beta,\frac{R\omega_{r}}{v}} \right)}v^{3}} \right)}{\partial\omega_{r}}} & (7)\end{matrix}$

1.3.3) Substituting the limit operating rotational speed ω_(rc) of thewind turbine generators into formula (5), calculating to obtain thelimit operating point of the wind turbine generators

$\left( {\omega_{rc},{0.5{\rho\pi}R^{2}{C_{P}\left( {\beta,\frac{R\omega_{rc}}{v}} \right)}v^{3}}} \right).$

Connecting the extreme operating points at each wind speed to form thestability boundary of the wind turbine generators, and substitutingformula (6) into formula (7) to calculate the limit tip speed ratioλ_(c). The limit tip speed ratio λ_(c) meets the following formula.

$\begin{matrix}{{3{K_{DL}\left( \frac{\lambda v}{R} \right)}^{2}} = {{{0.5}\rho\pi R^{2}\frac{\partial\left( {C_{P}\left( {\beta,\lambda} \right)} \right)}{\partial\frac{\lambda v}{R}}v^{3}} = {{0.5}\rho\pi R^{3}\frac{\partial\left( {C_{P}\left( {\beta,\lambda} \right)} \right)}{\partial\lambda}v^{2}}}} & (8)\end{matrix}$

1.3.5) Establishing the expression formula of the relationship betweenwind speed and rotor rotational speed on the stability boundary of thewind turbine generators, namely:

$\begin{matrix}{v = {\frac{R\omega_{r}}{\lambda_{c}}.}} & (9)\end{matrix}$

1.3.6) Substituting formula (9) into formula (5), and calculating toobtain the expression formula of the stability boundary of the windturbine generators, namely:

$\begin{matrix}{P_{c} = {{\frac{0.5{\rho\pi}R^{5}{C_{P}\left( {\beta,\lambda_{c}} \right)}}{\lambda_{c}^{3}}\omega_{r}^{3}} = {K_{c}{\omega_{r}^{3}.}}}} & (10)\end{matrix}$

1.3.7) Based on formula (10), updating the limit operating point of thewind turbine generators to (ω_(rc), K_(c)ω_(r) ³).

1.3.8) Establishing the stability constraints of the wind turbinegenerators when provides frequency response, and it is divided into thefollowing three situations.

I) When the wind turbine generator is operating at the lowest speed, thewind turbine generator does not provide frequency response. Thefrequency response of the wind turbine generator is as follows.

$\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} = {{0\omega_{r0}} < \omega_{\min}}} & (11)\end{matrix}$

In the above formulas, ω_(r0) is the rotor rotational speed in theinitial operating state of the wind turbine generators.

II) When the limit operating rotational speed ω_(rc) is less than thelowest speed ω_(min), the stability constraints of the wind turbinegenerators when provides frequency response are as follows.

$\begin{matrix}{{{K_{DL}\omega_{\min}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{f_{M}\left( \omega_{\min} \right)}\omega_{rc}} < \omega_{\min}} & (12)\end{matrix}$

In the above formulas, F_(M)(ω_(min)) is the mechanical power of thewind turbine generators at the lowest rotational speed ω_(min).

III) When ω_(rc)≥ω_(min), the stability constraints of the wind turbinegenerators when provides frequency response are as follows.

$\begin{matrix}{{{K_{DL}\omega_{rc}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {K_{c}\omega_{rc}^{3}}} & (13)\end{matrix}$

1.4) Establishing the output constraints of the wind turbine generatorswhen provides frequency response, and the main steps are as follows.

1.4.1) Updating the active output P_(E)* of the wind turbine generators,namely:

$\begin{matrix}{{P_{E} = {{\left( {1 - d_{w}} \right)P_{w}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}}}.} & (14)\end{matrix}$

In the above formulas, P_(w) is the available power of the wind turbinegenerators. d_(w) is the reserve coefficient of the wind turbinegenerators, and (1−d_(w))P_(w) is the actual output of the wind turbinegenerators when does not provide frequency response output.

1.4.2) Establishing the output constraints of the wind turbinegenerators when provides frequency response, namely:

$\begin{matrix}{{{\left( {1 - d_{w}} \right)P_{w}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {P_{w}^{\max}.}} & (15)\end{matrix}$

In the above formulas, P_(w) ^(max) is the maximum output of windturbine generators.

1.5) Combining formula (10), formula (12), formula (13) and formula(15), the security region of the wind turbine generators meets formula(16) to formula (19), namely:

$\begin{matrix}{{K_{w} = 0};{J_{w} = {{0\omega_{r0}} < \omega_{\min}}};} & (16)\end{matrix}$ $\begin{matrix}{{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}\omega_{rc}}} < \omega_{\min}};} & (17)\end{matrix}$ $\begin{matrix}{{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}\omega_{rc}}} \geq \omega_{\min}};{and}} & (18)\end{matrix}$ $\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {P_{w}^{\max} - {\left( {1 - d_{w}} \right){P_{w}.}}}} & (19)\end{matrix}$

2) Based on the security region of the wind turbine generators whenprovides frequency response, establishing a unit commitment modelconsidering the security region of the wind turbine generators. The mainsteps are as follows.

2.1) With the goal of minimizing the operating cost of the traditionalsynchronous generator, establishing the objective function, namely:

$\begin{matrix}{\min{\sum\limits_{i = 1}^{T}{\sum\limits_{g \in \zeta}{\left\lbrack {{\left( {{c_{g}P_{g,i}} + {c_{g}^{nl}N_{g,i}^{on}}} \right)\Delta t} + {c_{g}^{su}N_{g,i}^{su}}} \right\rbrack.}}}} & (20)\end{matrix}$

In the above formulas, ζ is a set of traditional synchronous generators.c_(g) is the marginal cost. c_(g) ^(nl) is the no-load cost. c_(g) ^(su)is the start-up cost. P_(g,i) is the active power of the traditionalsynchronous generator. N_(g,i) ^(on) is an online synchronous generator.N_(g,i) ^(su) is the synchronous generator turned on at step i. T is thetotal optimization time scale. Δt is the unit time interval. Variableswith the subscript i represent the variables of the i-th step. Variableswith subscript g represent variables related to traditional synchronousgenerator g. Variables with subscripts g,i represent the relatedvariables of the traditional synchronous generator g at the i-th step.

2) Establishing constraints of traditional unit commitment, whichinclude power flow constraints, synchronous generator constraints,system frequency stability constraints, frequency change rateconstraints, frequency lowest point constraints, and wind turbinegenerators security region constraints.

2.2.1) Power flow constraints are as follows.

$\begin{matrix}{{{\sum\limits_{g \in \zeta}P_{g,i}} + {\sum\limits_{w \in W}{\left( {1 - d_{w,i}} \right)P_{w,i}}}} = {{L_{i}i} \in T}} & (21)\end{matrix}$

In the above formulas, W is a set of wind turbine generators. L_(i) isthe total load of the system. The wind turbine generators parameters areall aggregate parameters. Variables with subscript w represent variablesrelated to wind turbine generators w. Variables with subscripts w,irepresent related variables of wind turbine generators w at step i.

2.2.2) Synchronous generator constraints are shown in formula (22) toformula (28).

$\begin{matrix}{{N_{g,i}^{on}P_{g}^{\min}} \leq P_{g,i} \leq {N_{g,i}^{on}P_{g}^{\max}}} & (22)\end{matrix}$ $\begin{matrix}{N_{g,i}^{on} = {N_{g,{i - 1}}^{on} + {N_{g,i}^{su}{\_ N}_{9^{j}}^{sd}}}} & (23)\end{matrix}$ $\begin{matrix}{N_{g,i}^{on} = {N_{g,{i - 1}}^{on} + {N_{g,i}^{su}{\_ N}_{9^{j}}^{sd}}}} & (24)\end{matrix}$ $\begin{matrix}{{P_{g,i} - P_{g,{i - 1}}} \leq {{\Delta P_{g}^{\max}N_{g,{i - 1}}^{on}} + {\Delta{P_{g}^{{su}\max}\left( {N_{g,i}^{on} - N_{g,{i - 1}}^{on}} \right)}}}} & (25)\end{matrix}$ $\begin{matrix}{{P_{g,i} - P_{g,{i - 1}}} \geq {{{- \Delta}P_{g}^{\max}N_{g,i}^{on}} + {\Delta{P_{g}^{sdmax}\left( {N_{g,i}^{on} - N_{g,{i - 1}}^{on}} \right)}}}} & (26)\end{matrix}$ $\begin{matrix}{{\sum\limits_{k = {i + 1 - {\Delta t_{g}^{up}}}}^{i}N_{g,k}^{su}} \leq N_{g,i}^{on}} & (27)\end{matrix}$ $\begin{matrix}{{\sum\limits_{k = {i + 1 - {\Delta t_{g}^{dw}}}}^{i}N_{g,k}^{sd}} \leq N_{g,i}^{off}} & (28)\end{matrix}$

In the above formulas, P_(g) ^(min) and P_(g) ^(max) are the minimumvalue and maximum value of the synchronous generator output,respectively. ΔP_(g) ^(max) is the maximum value of the output change ofthe synchronous generator. ΔP_(g) ^(su max) and ΔP_(g) ^(sd max) are themaximum upward and downward climbing power of the synchronous generator,respectively. N_(g, i) ^(sd) is the number of synchronous generatorsshut down in step i. N_(g,i) ^(off) is the number of synchronousgenerators offline at step i. Δt_(g) ^(up) and Δt_(g) ^(dw) are theminimum start and stop time of the unit. i∈T. g∈ζ.

2.2.3) The system frequency stability constraints are as follows.

$\begin{matrix}{{{2H_{i}\frac{d\Delta f}{dt}} + {\left( {{D_{i}L_{i}} + K_{i}} \right)\Delta f}} = {{- \Delta}L_{i}}} & (29)\end{matrix}$

Wherein, D_(i) is the load damping coefficient. H_(i) is the systeminertia time constant. K_(i) is the frequency response coefficient.

Wherein, the system inertia time constant H_(i) is shown as follows.

$\begin{matrix}{H_{i} = {\frac{\sum\limits_{g \in \zeta}{H_{g}P_{g}^{\max}N_{g,i}^{on}}}{f_{0}} + {\pi{\sum\limits_{w \in W}J_{w,i}}}}} & (30)\end{matrix}$

In the above formulas, H_(g) is the inertia time coefficient ofsynchronous generator. The optimized variables in formula (30) are thevirtual inertia control parameters J_(w,i) of the online synchronousgenerator N_(g, i) ^(on) and the wind turbine generators at i-th step.f₀ is the reference frequency of the power system.

The frequency response coefficient K_(i) controlled by the P-f of thesynchronous generator and wind turbine generators is shown as follows.

$\begin{matrix}{K_{i} = {\frac{\sum\limits_{g \in \zeta}{K_{g}P_{g}^{\max}N_{g,i}^{on}}}{f_{0}} + {2\pi{\sum\limits_{w \in W}K_{w,i}}}}} & (31)\end{matrix}$

In the above formulas, K_(g)=1/K_(droop-g). K_(droop-g) is the droopcontrol parameter of the synchronous generator. The optimized variablesin formula (31) are the frequency response parameter K_(w,i) of theonline synchronous generator N_(g, i) ^(on) and the wind turbinegenerators at the i-th step.

System frequency deviation Δf is shown as follows.

$\begin{matrix}{{\Delta{f(t)}} = \frac{\left( {e^{{- \frac{({{D_{i}L} + K_{i}})}{2H_{i}}}t} - 1} \right)\Delta L_{l}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} & (32)\end{matrix}$

Frequency change rate dΔf/dt is shown as follows.

$\begin{matrix}{\frac{d\Delta{f(t)}}{dt} = {{- \frac{\Delta L_{i}}{2H_{i}}}e^{\frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}t}}} & (33)\end{matrix}$

2.2.4) Frequency change rate constraints are shown as follows.

$\begin{matrix}{{❘\left( \frac{d\Delta{f(t)}}{dt} \right)❘} \leq \frac{\Delta L_{i}}{2H_{i}} \leq \left( \frac{d\Delta f}{dt} \right)_{\max}} & (34)\end{matrix}$

2.2.5) Frequency lowest point constraints are shown as follows.

$\begin{matrix}{{{❘{\Delta{f(t)}}❘} \leq {❘{\Delta f_{{nadir},i}}❘}} = {\frac{\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)} \leq {\Delta f_{\max}}}} & (35)\end{matrix}$

2.2.6) Based on formula (1), formula (2), formula (32) to formula (35),establishing the equation of frequency response provided by the windturbine generators, namely:

$\begin{matrix}{{{{- K_{w,i}}\Delta{f(t)}} - {J_{w,i}\frac{d\Delta{f(t)}}{dt}}} = {{{{- K_{w,i}}\frac{\left( {e^{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}} - 1} \right)\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} + {J_{w,i}\frac{\Delta L_{i}}{2H_{i}}e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}}} = {{{\left( {{- \frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} + \frac{J_{w,i}\Delta L_{i}}{2H_{i}}} \right)e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}} + \frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} \leq {\max\left\{ {\frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)},\frac{J_{w,i}\Delta L_{i}}{2H_{i}}} \right\}} \leq {\max{\left\{ {{K_{w,i}\Delta f_{\max}},{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max}} \right\}.}}}}} & (36)\end{matrix}$

2.2.7) Substituting formula (36) into formula (17) to formula (19) toestablish the security region constraints of the wind turbinegenerators, which are shown as formula (37) to formula (43)respectively.

$\begin{matrix}{{K_{w} = 0};{J_{w} = {{0\omega_{r0}} < \omega_{\min}}}} & (37)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}\omega_{rc}}} < \omega_{\min}} & (38)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}\omega_{rc}}} < \omega_{\min}} & (39)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}\omega_{rc}}} \geq \omega_{\min}} & (40)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}\omega_{rc}}} \geq \omega_{\min}} & (41)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {P_{w}^{\max} - {\left( {1 - d_{w,i}} \right)P_{w,i}}}} & (42)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {P_{w}^{\max} - {\left( {1 - d_{w,i}} \right)P_{w,i}}}} & (43)\end{matrix}$

3) Calculating the unit commitment model considering the wind turbinegenerators security region by using mixed-integer linear programmingmethod, to obtain the operation result of the unit commitmentconsidering the wind turbine generators security region with frequencyresponse control.

Embodiment 1

An experiment to verify the unit commitment method considering the windturbine generators security region with frequency response control,mainly comprises the following steps.

1) Taking the UK 2030 power system (GB 2030 power system) as testsystem. Information of the synchronous generator is shown in Table 1.

TABLE 1 Related parameters of the synchronous generator nuclear powerclosed loop open loop plant set gas turbine gas turbine number of units4 100 30 rated capacity (MW) 1800 500 100 minimum output (MW) 1400 25050 no-load cost c_(g) ^(nl) (£/h) 0 4500 3000 marginal cost c_(g) ^(m)(£/MWh) 10 47 200 start-up cost c_(g) ^(st) (£) — 10000 0 duration time(h) — 4 4 inertial time coefficient 5 4 4 H_(g) (s) droop controlparameters 0.2 0.2 0.2 K_(droop-g) maximum one-time — 10% 10% FM outputramping rate (MW/h) 360 100 20

The maximum and minimum load requirements of the system are 30 GW and 60GW. The capacity of a single wind turbine generators is 1.5 MW, and thetotal wind power capacity of the system changes according to demand. Ineach case, the total wind power output accounts for about 35% of theload. The load damping parameter is set to D=0.5%/Hz. Considering thetypical N−1 failure scenario, the maximum power fluctuation of thesystem is the push operation of the synchronous unit with the largestcapacity ΔL_(max)=1800 MW. The limit value of the frequency drop rate is(dΔf/dt)_(max)=0.5 Hz/s, and the lowest point of the frequency isΔf_(nadir)=0.5 Hz/s. The unit commitment is solved by gurobi.

2) Determining the Influence of Wind Turbine Generators Security Regionon Unit Commitment.

It can be seen from FIG. 1 that the security region of wind turbinegenerators changes with the changes of wind speed, and the securityregion has different effective constraints under different wind speeds.In this embodiment, the distribution of effective constraints atdifferent wind speeds is shown in Table 2. In the FIG. 1 , line Arepresents the rotor rotational speed constraints, line B represents thestability boundary constraints, and line C represents the outputconstraints. The wind speed is shown in FIG. 2 , wherein line Drepresents the rated wind speed.

TABLE 2 Distribution of effective constraints at different wind speedswind speed(m/s) 7.2< 7.2-9 >9 effective rotor stability outputconstraints rotational constraints constraint speed constraints

Therefore, the period of effective constraint distribution is asfollows.

TABLE 3 Period distribution of effective constraints dispatch point 6-154-6, 16-18 0-3, 19-23 effective rotor stability output constraintsrotational constraints constraints speed constraints

It can be seen from Table 2 and Table 3 that in the high wind speedsection, the security region constraints are mainly determined by theoutput constraints. In the medium wind speed section, the securityregion constraints are mainly determined by the stability constraints.In the low wind speed section, the security region constraints aremainly determined by the rotor rotational speed constraints. Thesecurity region of the wind turbine generators when provides inertiaresponse changes with the changes of wind speed. Therefore, the inertiaresponse parameter of the wind turbine generators should not be set to afixed value, but should be optimized in real time with changes of windspeed and system status.

The system frequency indexes are shown in FIG. 3 . RoCoF and FN are thesystem frequency conditions when the security region is not considered,and RoCoF-SR and FN-SR are the system frequency conditions when thesecurity region is considered. It can be seen from FIG. 3 that themethod provided by the present invention can meet the needs of systemfrequency stability. The frequency response output of wind turbinegenerators is shown in FIG. 4 . Wherein, SR is the security region ofthe wind turbine generators when provides frequency response, PFR and IRrespectively are the frequency response output of the wind turbinegenerators when the security region is not considered, and PFR-SR andIR-SR respectively are the frequency response output of the wind turbinegenerators when the security region is considered.

It can be seen from FIG. 3 that when the security region of wind turbinegenerators is not considered, the frequency response output of windturbine generators at dispatching points 1-3 and 21-23 will exceed thesecurity region of the wind turbine generators, which may cause the windturbine generators cannot be safely and stably operated, or willoverestimate the frequency response capability of the wind turbinegenerators and causes the frequency response output of the wind turbinegenerators cannot meet the system frequency requirements, and resultingsystem frequency becoming unstable. The method provided by the presentinvention can simultaneously meet the system frequency stability and thewind turbine generators security region requirements, and ensure thesafe and stable operation of the system.

3) The Influence of Wind Turbine Generators Reserve Capacity onFrequency Response Output.

When considering the reserve capacity of wind turbine generators, itsfrequency response output is shown in FIG. 5 . Wherein, SR-D is thesecurity region constraints when considering the reserve capacity, andPFR-D and IR-D respectively are the frequency response output of thewind turbine generators when considering the reserve.

According to the analysis in the previous section, the main effectiveconstraints of this embodiment are the output constraints of the windturbine generators. Therefore, when the wind power has a certain amountof reserve capacity, it can effectively expand the security region ofthe wind turbine generators, thereby improving the ability of the windturbine generators to provide frequency response.

To ensure the stability of the system frequency, when the wind turbinegenerators inertia response is insufficient, more synchronous generatorsneed to be launched. Since the synchronous generators are restricted byminimum output and climbing constraints, the launch of a large number ofsynchronous generators will compress the penetration rate of windturbine generators and cause a large amount of wind curtailment.

In this embodiment, the wind power utilization rate is shown in Table 4,and the wind power utilization rate unlisted dispatching points is 100%.At the dispatch points of 0-2 and 23, due to the influence of thermalpower climbing constraints, it is impossible to fully balance thefluctuations of the wind turbine generators output, which results inpartial wind power curtailment. During this time period, the curtailedwind can be fully utilized as a reserve. Other dispatching points needto sacrifice part of the wind power output as reserve capacity. It canbe seen from Table 4 that after considering the reserve of wind turbinegenerators, although part of the wind power output is reduced, thesecurity region of wind power is expanded, and the inertia responsecapability of wind turbine generators is enhanced, which reduces thepressure of synchronous generators to provide frequency response,thereby reducing the number of online synchronous power generator, andincreasing the utilization rate of wind power output.

The method provided by the present invention can effectively optimizethe wind power reserve capacity and fully guarantee the wind powerutilization rate.

TABLE 4 Wind power utilization rate dispatching points 0 1 2 3 4 19 2122 23 security region constraints are not considered 95% 88% 88% 100%100% 100% 100%  100%  98% security region constraints are considered,52% 22% 64%  77%  91%  97% 81% 42% 41% and reserve is not consideredboth security region constraints and reserve 95% 88% 88% 100% 100% 100%98% 95% 95% are considered

From the experimental results, it can be seen that the unit commitmentmethod considering the security region of wind turbine generators withfrequency response control proposed by the present invention can ensurethe safe operation of the wind turbine generators while meeting theneeds of system frequency stability, and can make full use of thereserve capacity of the wind turbine generators to improve the abilityof providing frequency response by the wind turbine generators, improvewind power utilization and reduce the wind curtailment.

In summary, the present invention proposes a unit commitment methodconsidering both frequency stability and safe operation of wind turbinegenerators. Comprehensively considering the stability constraints,rotational speed constraints and output constraints of wind turbinegenerators, and the security region of wind turbine generators whenprovides frequency response is deduced. With the goal of minimizing theoperating cost of synchronous generator, the system frequency stabilityconstraints and wind turbine generators security region constraints areadded to the traditional unit commitment model to achieve economic,stable and safe operation of the entire system. The study of theembodiment shows that the method provided by the present invention caneffectively guarantee the stability of the system frequency and the safeoperation of wind turbine generators. It can make full use of wind powerresources by optimizing the reserve capacity of wind turbine generators,and can provide guidance to the set of frequency response parameters ofwind turbine generators and the unit commitment consideringhigh-penetration wind turbine generators.

The invention claimed is:
 1. A unit commitment method considering asecurity region of wind turbine generators with frequency responsecontrol, mainly comprises the following steps: 1) determining thesecurity region of wind turbine generators when the wind turbinegenerators provide a frequency response; 2) based on the security regionof the wind turbine generators when the wind turbine generators providethe frequency response, establishing a unit commitment model consideringthe security region of the wind turbine generators; and 3) calculatingthe unit commitment model considering the security region of the windturbine generators by using mixed-integer linear programming method, andobtaining the operation result of the unit commitment considering thesecurity region of the wind turbine generators with frequency responsecontrol; wherein the main steps of determining security region of windturbine generators when the wind turbine generators provide thefrequency response are as follows: 1) establishing an output model ofwind turbine generators when the wind turbine generators provide thefrequency response, namely: $\begin{matrix}{{\Delta P_{w}^{PFR}} = {K_{w}\Delta f{and}}} & (1)\end{matrix}$ $\begin{matrix}{{\Delta P_{w}^{IR}} = {J_{w}\frac{d\Delta f}{dt}}} & (2)\end{matrix}$ in the above formulas, ΔP_(w) ^(PFR) and ΔP_(w) ^(IR)respectively represent a primary frequency response and a virtualinertia response provided by the wind turbine generators; frequencyresponse coefficient K_(w)=1/K_(droop-w); K_(droop-w) is droop controlparameter of the wind turbine generators in primary frequency responsecontrol; J_(w) is virtual inertia control parameter of the wind turbinegenerators; Δf is system frequency deviation, and t refers to time; 2)establishing constraint condition of rotor rotational speed ω_(r),namely:ω_(min)≤ω_(r)≤ω_(max)  (3) in the above formulas, ω_(min) and ω_(max)respectively are the lowest speed and highest speed of the rotorrotational speed of the wind turbine generators; 3) establishingconstraint conditions of wind power stability, and the main steps are asfollows: 3.1) determining synchronization characteristics of the windturbine generators, namely: $\begin{matrix}{P_{E} = {{K_{DL}\omega_{r}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}{and}}}} & (4)\end{matrix}$ $\begin{matrix}{{P_{E} = {P_{M} = {{0.5}\rho\pi R^{2}{C_{P}\left( {\beta,\lambda} \right)}v^{3}}}};} & (5)\end{matrix}$ in the above formulas, P_(E) is active output of the windturbine generators; K_(DL) is de-load factor of the wind turbinegenerators; when the wind turbine generators are working at maximumpower tracking mode, coefficient K_(DL) is the maximum power trackingcoefficient, K_(DL)ω_(r) ³ is the output of the wind turbine generatorswhen there is no virtual inertia response; ρ is air density; R isdiameter of the rotor of the wind turbine generators; v is wind speed;C_(p) is power coefficient of the wind turbine generators; P_(M) ismechanical power of the wind turbine generators; and β is pitch angle ofthe wind turbine generators; wherein, the tip speed ratio λ is shown asfollows: $\begin{matrix}{\lambda = \frac{R\omega_{r}}{v}} & (6)\end{matrix}$ 3.2) determining limit operating rotational speed ω_(rc)of the wind turbine generators, and the limit operating rotational speedω_(rc) of the wind turbine generators meets the following formula:$\begin{matrix}{\frac{\partial\left( {{K_{DL}\omega_{r}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \right)}{\partial\omega_{r}} = \frac{\partial\left( {0.5{\rho\pi}R^{2}{C_{P}\left( {\beta,\frac{R\omega_{r}}{v}} \right)}v^{3}} \right)}{\partial\omega_{r}}} & (7)\end{matrix}$ 3.3) substituting the limit operating rotational speedω_(rc) of the wind turbine generators into formula (5), and calculatingto obtain limit operating point of the wind turbine generators$\left( {\omega_{rc},{0.5\rho\pi R^{2}{C_{P}\left( {\beta,\frac{R\omega_{rc}}{v}} \right)}v^{3}}} \right);$3.4) connecting extreme operating points at each wind speed to formstability boundary of the wind turbine generators, and substitutingformula (6) into formula (7), and calculating limit tip speed ratioλ_(c); and the limit tip speed ratio λ_(c) meets the following formula:$\begin{matrix}{{3{K_{DL}\left( \frac{\lambda v}{R} \right)}^{2}} = {{{0.5}\rho\pi R^{2}\frac{\partial\left( {C_{P}\left( {\beta,\lambda} \right)} \right)}{\partial\frac{\lambda v}{R}}v^{3}} = {{0.5}\rho\pi R^{3}\frac{\partial\left( {C_{P}\left( {\beta,\lambda} \right)} \right)}{\partial\lambda}v^{2}}}} & (8)\end{matrix}$ 3.5) establishing expression formula of the relationshipbetween wind speed and rotor rotational speed on the stability boundaryof the wind turbine generators, namely: $\begin{matrix}{{v = \frac{R\omega_{r}}{\lambda_{c}}};} & (9)\end{matrix}$ 3.6) substituting formula (9) into formula (5), andcalculating to obtain expression formula of the stability boundary ofthe wind turbine generators, namely: $\begin{matrix}{P_{c} = {{\frac{0.5{\rho\pi}R^{5}{C_{P}\left( {\beta,\lambda_{c}} \right)}}{\lambda_{c}^{3}}\omega_{r}^{3}} = {K_{c}\omega_{r}^{3}}}} & (10)\end{matrix}$ 3.7) based on formula (10), updating the limit operatingpoint of the wind turbine generators to (ω_(rc), K_(c)ω_(r) ³); 3.8)establishing stability constraints of the wind turbine generators whenthe wind turbine generators provide the frequency response, and it isdivided into the following three situations: I) when the wind turbinegenerators are operating at the lowest speed, the wind turbinegenerators do not provide the frequency response, and the frequencyresponse of the wind turbine generators is as follows: $\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} = {{0\omega_{r0}} < \omega_{\min}}} & (11)\end{matrix}$ in the above formulas, ω_(r0) is the rotor rotationalspeed in initial operating state of the wind turbine generators; II)when the limit operating rotational speed ω_(rc) is less than the lowestspeed ω_(min), the stability constraints of the wind turbine generatorswhen the wind turbine generators provide the frequency response are asfollows: $\begin{matrix}{{{K_{DL}\omega_{\min}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{f_{M}\left( \omega_{\min} \right)}\omega_{rc}} < \omega_{\min}} & (12)\end{matrix}$ in the above formulas, f_(M)(ω_(min)) is the mechanicalpower of the wind turbine generators at the lowest rotational speedω_(min); III) when ω_(rc)≥ω_(min), the stability constraints of the windturbine generators when the wind turbine generators provide thefrequency response are as follows: $\begin{matrix}{{{K_{DL}\omega_{rc}^{3}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {K_{c}\omega_{rc}^{3}}} & (13)\end{matrix}$ 4) establishing output constraints of the wind turbinegenerators when the wind turbine generators provide the frequencyresponse, and the main steps are as follows: 4.1) updating the activeoutput P_(E)* of the wind turbine generators, namely: $\begin{matrix}{{P_{E}^{*} = {{\left( {1 - d_{w}} \right)P_{w}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}}};} & (14)\end{matrix}$ in the above formulas, P_(w) is available power of thewind turbine generators; d_(w) is reserve coefficient of the windturbine generators, and (1−d_(w))P_(w) is actual output of the windturbine generators when does not provide the frequency response output;4.2) establishing output constraints of the wind turbine generators whenthe wind turbine generators provide the frequency response, namely:$\begin{matrix}{{{\left( {1 - d_{w}} \right)P_{w}} - {K_{w}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq P_{w}^{\max}} & (15)\end{matrix}$ in the above formulas, P_(w) ^(max) is the maximum outputof wind turbine generators; 5) combining formula (10), formula (12),formula (13) and formula (15), the security region of the wind turbinegenerators meets formula (16) to formula (19), namely: $\begin{matrix}\begin{matrix}{{K_{w} = 0};{J_{w} = 0}} & {{\omega_{r0} < \omega_{\min}};}\end{matrix} & (16)\end{matrix}$ $\begin{matrix}\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\omega_{\min}^{3}}}} & {{\omega_{rc} < \omega_{\min}};}\end{matrix} & (17)\end{matrix}$ $\begin{matrix}\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\omega_{rc}^{3}}}} & {{\omega_{rc} \geq \omega_{\min}};{and}}\end{matrix} & (18)\end{matrix}$ $\begin{matrix}{{{{- K_{w}}\Delta f} - {J_{w}\frac{d\Delta f}{dt}}} \leq {P_{w}^{\max} - {\left( {1 - d_{w}} \right){P_{w}.}}}} & (19)\end{matrix}$ wherein the main steps of establishing a unit commitmentmodel considering the security region of the wind turbine generators areas follows: 1) With the goal of minimizing the operating cost of thetraditional synchronous generator, establishing the objective function,namely: $\begin{matrix}\begin{matrix}\min & {{\overset{T}{\sum\limits_{i = 1}}{\sum\limits_{g \in \zeta}\left\lbrack {{\left( {{c_{g}P_{g,i}} + {c_{g}^{nl}N_{g,i}^{on}}} \right)\Delta t} + {c_{g}^{su}N_{g,i}^{su}}} \right\rbrack}};}\end{matrix} & (20)\end{matrix}$ in the above formulas, ζ is a set of traditionalsynchronous generators; c_(g) is marginal cost; c_(g) ^(nl) is no-loadcost; c_(g) ^(su) is start-up cost; P_(g,i) is active power of thetraditional synchronous generator; N_(g,i) ^(on) is online synchronousgenerator; N_(g,i) ^(su) is synchronous generator turned on at step i; Tis total optimization time scale; Δt is unit time interval; variableswith the subscript i represent variables of the i-th step; variableswith subscript g represent variables related to traditional synchronousgenerator g; variables with subscripts g,i represent related variablesof the traditional synchronous generator g at the i-th step; 2)establishing constraints of traditional unit commitment, which includepower flow constraints, synchronous generator constraints, systemfrequency stability constraints, frequency change rate constraints,frequency lowest point constraints, and wind turbine generators securityregion constraints; 2.1) power flow constraints are as follows:$\begin{matrix}\begin{matrix}{{{\sum\limits_{g \in \zeta}P_{g,i}} + {\sum\limits_{w \in W}{\left( {1 - d_{w,i}} \right)P_{w,i}}}} = L_{i}} & {i \in T}\end{matrix} & (21)\end{matrix}$ in the above formulas, W is a set of wind turbinegenerators; L_(i) is total load of the system; the wind turbinegenerators parameters are all aggregate parameters; variables withsubscript w represent variables related to wind turbine generators w;variables with subscripts w,i represent related variables of windturbine generators w at step i; 2.2) synchronous generator constraintsare shown in formula (22) to formula (28); $\begin{matrix}{{N_{g,i}^{on}P_{g}^{\min}} \leq P_{g,i} \leq {N_{g,i}^{on}P_{g}^{\max}}} & (22)\end{matrix}$ $\begin{matrix}{N_{g,i}^{on} = {N_{g,{i - 1}}^{on} + N_{g,i}^{su} - N_{g,i}^{sd}}} & (23)\end{matrix}$ $\begin{matrix}{N_{g,i}^{off} = {N_{g,{i - 1}}^{off} + N_{g,i}^{sd} - N_{g,i}^{su}}} & (24)\end{matrix}$ $\begin{matrix}{{P_{g,i} - P_{g,{i - 1}}} \leq {{\Delta P_{g}^{\max}N_{g,{i - 1}}^{on}} + {\Delta{P_{g}^{{su}\max}\left( {N_{g,i}^{on} - N_{g,{i - 1}}^{on}} \right)}}}} & (25)\end{matrix}$ $\begin{matrix}{{P_{g,i} - P_{g,{i - 1}}} \geq {{{- \Delta}P_{g}^{\max}N_{g,i}^{on}} + {\Delta{P_{g}^{{sd}\max}\left( {N_{g,{i - 1}}^{on} - N_{g,i}^{on}} \right)}}}} & (26)\end{matrix}$ $\begin{matrix}{{\underset{k = {i + 1 - {\Delta t_{g}^{up}}}}{\sum\limits^{i}}N_{g,k}^{su}} \leq N_{g,i}^{on}} & (27)\end{matrix}$ $\begin{matrix}{{\overset{i}{\sum\limits_{k = {i + 1 - {\Delta t_{g}^{dw}}}}}N_{g,k}^{sd}} \leq N_{g,i}^{off}} & (28)\end{matrix}$ in the above formulas, P_(g) ^(min) and P_(g) ^(max) arethe minimum value and maximum value of the synchronous generator output,respectively; ΔP_(g) ^(max) is the maximum value of output change of thesynchronous generator; ΔP_(g) ^(su max) and ΔP_(g) ^(sd max) are themaximum upward and downward climbing power of the synchronous generator,respectively; N_(g,i) ^(sd) is the number of synchronous generators shutdown in step i; N_(g,i) ^(off) is the number of synchronous generatorsoffline at step i; Δt_(g) ^(up) and Δt_(g) ^(up) are the minimum startand stop time of the unit; i∈T; g∈ζ; 2.3) the system frequency stabilityconstraints are as follows: $\begin{matrix}{{{2H_{i}\frac{d\Delta f}{dt}} + {\left( {{D_{i}L_{i}} + K_{i}} \right)\Delta f}} = {{- \Delta}L_{i}}} & (29)\end{matrix}$ wherein, D_(i) is the load damping coefficient; H_(i) isthe system inertia time constant; K_(i) is the frequency responsecoefficient; wherein, the system inertia time constant H_(i) is shown asfollows: $\begin{matrix}{H_{i} = {\frac{\sum\limits_{g \in \zeta}{H_{g}P_{g}^{\max}N_{g,i}^{on}}}{f_{0}} + {\pi{\sum\limits_{w \in W}J_{w,i}}}}} & (30)\end{matrix}$ in the above formulas, H_(g) is the inertia timecoefficient of synchronous generator; The optimized variables in formula(30) are the virtual inertia control parameters J_(w,i) of the onlinesynchronous generator N_(g,i) ^(on) and the wind turbine generators ati-th step; f₀ is the reference frequency of the power system; frequencyresponse coefficient K_(i) is shown as follows: $\begin{matrix}{K_{i} = {\frac{\sum\limits_{g \in \zeta}{K_{g}P_{g}^{\max}N_{g,i}^{on}}}{f_{0}} + {2\pi{\sum\limits_{w \in W}K_{w,i}}}}} & (31)\end{matrix}$ in the above formulas, K_(g)=1/K_(droop-g); K_(droop-g) isthe droop control parameter of the synchronous generator; the optimizedvariables in formula (31) are the frequency response parameter K_(w,i)of the online synchronous generator N_(g,i) ^(on) and the wind turbinegenerators at the i-th step; system frequency deviation Δf is shown asfollows: $\begin{matrix}{{\Delta{f(t)}} = \frac{\left( {e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t} - 1} \right)\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} & (32)\end{matrix}$ frequency change rate dΔf/dt is shown as follows:$\begin{matrix}{\frac{d\Delta{f(t)}}{dt} = {{- \frac{\Delta L_{i}}{2H_{i}}}e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}}} & (33)\end{matrix}$ 2.4) frequency change rate constraints are shown asfollows: $\begin{matrix}{{❘\left( \frac{d\Delta{f(t)}}{dt} \right)❘} \leq \frac{\Delta L_{i}}{2H_{i}} \leq \left( \frac{d\Delta f}{dt} \right)_{\max}} & (34)\end{matrix}$ 2.5) frequency lowest point constraints are shown asfollows: $\begin{matrix}{{{❘{\Delta{f(t)}}❘} \leq {❘{\Delta f_{{nadir},i}}❘}} = {\frac{\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)} \leq {\Delta f_{\max}}}} & (35)\end{matrix}$ 2.6) Based on formula (1), formula (2), formula (32) toformula (35), establishing the equation of the frequency responseprovided by the wind turbine generators, namely: $\begin{matrix}{{{- K_{w,i}}\Delta{f(t)}} - {J_{w,i}\frac{d\Delta{f(t)}}{dt}}} & (36)\end{matrix}$$= {{{- K_{w,i}}\frac{\left( {e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t} - 1} \right)\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} + {J_{w,i}\frac{\Delta L_{i}}{2H_{i}}e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}}}$$= {{\left( {{- \frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}} + \frac{J_{w,i}\Delta L_{i}}{2H_{i}}} \right)e^{{- \frac{({{D_{i}L_{i}} + K_{i}})}{2H_{i}}}t}} + \frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i}} \right)}}$$\leq {\max\left\{ {\frac{K_{w,i}\Delta L_{i}}{\left( {{D_{i}L_{i}} + K_{i)}} \right.},\frac{J_{w,i}\Delta L_{i}}{2H_{i}}} \right\}}$${\leq {\max\left\{ {{K_{w,i}\Delta f_{\max}},{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max}} \right\}}};$2.7) substituting formula (36) into formula (17) to formula (19) toestablish the security region constraints of the wind turbinegenerators, which are shown as formula (37) to formula (43)respectively: $\begin{matrix}{{K_{w} = 0};{J_{w} = \begin{matrix}0 & {\omega_{r0} < \omega_{\min}}\end{matrix}}} & (37)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\begin{matrix}\omega_{\min}^{3} & {\omega_{rc} < \omega_{\min}}\end{matrix}}}} & (38)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {{f_{M}\left( \omega_{\min} \right)} - {K_{DL}\begin{matrix}\omega_{\min}^{3} & {\omega_{rc} < \omega_{\min}}\end{matrix}}}} & (39)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\begin{matrix}\omega_{rc}^{3} & {\omega_{rc} \geq \omega_{\min}}\end{matrix}}}} & (40)\end{matrix}$ $\begin{matrix}{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {{K_{c}\omega_{rc}^{3}} - {K_{DL}\begin{matrix}\omega_{rc}^{3} & {\omega_{rc} \geq \omega_{\min}}\end{matrix}}}} & (41)\end{matrix}$ $\begin{matrix}{{K_{w,i}\Delta f_{\max}} \leq {P_{w}^{\max} - {\left( {1 - d_{w,i}} \right)P_{w,i}}}} & (42)\end{matrix}$ $\begin{matrix}{{{J_{w,i}\left( \frac{d\Delta f}{dt} \right)}_{\max} \leq {P_{w}^{\max} - {\left( {1 - d_{w,i}} \right)P_{w,i}}}};} & (43)\end{matrix}$ wherein frequency response control parameters of the windturbine generators are set based on the security region of the windturbine generators when the wind turbine generators provide thefrequency response.